585970 ÷ 45 
We're looking to find how many times 45 goes into 585970.

Advancing to step 1:
The number 45 fits into 5 0 times, leaving a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 45

Step 2:
If we divide 58 by 45, we get 1 and a remainder of 13.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 45 from 58 to get 13.
Fetch the next digit (5) from the dividend, attach it to 13 and continue: 135 / 45

Advancing to step 3:
The number 45 fits into 135 3 times, leaving a remainder of 0.
The next digit of our result is 3. 
Result so far: 13.0
If we subtract 135 from 135, we get 0.
Take the next digit (9) from the dividend and append it to 0, then repeat: 9 / 45

Going ahead to step 4:
If we divide 9 by 45, we get 0 and a remainder of 9.
The next digit of our result is 0. 
Result so far: 130.0
Subtract 0 from 9 to get 9.
Bring next digit (7) of the dividend behind the 9 and repeat the process: 97 / 45

Advancing to step 5:
The number 45 fits into 97 2 times, leaving a remainder of 7.
The number 2 becomes the next digit in our result. 
Result so far: 1302.0
Subtracting 90 from 97 leaves us with 7.
Include the next digit (0) from the dividend after 7, then repeat: 70 / 45

Moving on to step 6:
If we divide 70 by 45, we get 1 and a remainder of 25.
Put 1 as the next digit of the answer. 
Result so far: 13021.0
Subtract 45 from 70 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 7:
250 divided by 45 is 5 with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 13021.5
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
250 divided by 45 is 5 with a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 13021.55
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The quotient of the division is 13021.55, and the remainder is 0.025.